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中文摘要：
与传统的基于流形的数据分类算法大都假设数据位于同一个流形上不同,假设多类数据分别位于不同的流形上。提出了一种基于多流形的数据分类算法,算法大致分为两步：学习过程和测试过程。学习过程采用线性流形学习方法获得训练数据的低维坐标和映射矩阵,测试阶段则利用嵌入空间中对应测试数据点与其k个邻域点的重构误差值来决定其类别。在人工合成数据和coil-20数据库上的实验都表明了该算法的有效性。
英文摘要：
Unlike most traditional manifold-based data classification algorithms assume that all the data points are on a single manifold,it supposes that multiple classes data may reside on different manifolds.A data classification algorithm on multiple manifolds is presented.The algorithm roughly divides into two steps：learning process and testing process.In learning process,the manifolds are firstly learned for each class separately using linear manifold learning,and then low dimensionality coordinates and mapping matrix of the training data is obtained.In testing process,classification is performed using minimum reconstruction error between test data and its k-nearest neighbors in embedding space.The experimental results on both synthetic data and coil-20 databases show the effectiveness of the proposed algorithm.
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